1. Unless otherwise noted, the content of this course material is licensed under a Creative Commons Attribution 3.0 License. http://creativecommons.org/licenses/by/3.0/ © 2009, Peter Von Buelow You assume all responsibility for use and potential liability associated with any use of the material. Material contains copyrighted content, used in accordance with U.S. law. Copyright holders of content included in this material should contact open.michigan@umich.edu with any questions, corrections, or clarifications regarding the use of content. The Regents of the University of Michigan do not license the use of third party content posted to this site unless such a license is specifically granted in connection with particular content. Users of content are responsible for their compliance with applicable law. Mention of specific products in this material solely represents the opinion of the speaker and does not represent an endorsement by the University of Michigan. For more information about how to cite these materials visit https://open.umich.edu/education/about/terms-of-use. Any medical information in this material is intended to inform and educate and is not a tool for self-diagnosis or a replacement for medical evaluation, advice, diagnosis or treatment by a healthcare professional. You should speak to your physician or make an appointment to be seen if you have questions or concerns about this information or your medical condition. Viewer discretion is advised: Material may contain medical images that may be disturbing to some viewers.

2. ARCHITECTURE 324 STRUCTURES II Lecture Topics : Course Syllabus Chapter 11 – Wood Beams University of Michigan, TCAUP Structures II Slide 2/27 Teaching Staff: Prof. Peter von Buelow GSI’s: Donaghy, Ryan Drew, Thomas Ducharme-Smith, Matt Lindstrom, Michael Ozor, Chigozie Amara Source: I. Engel. Structural principles. Englewood Cliffs, N.J. : Prentice-Hall, 1984

3. Course Syllabus Organization Lecture – Monday & Friday Recitation – Wednesday Exercises – from textbook Problems – on web Evaluation Tests 39% Problems 48% Project 13% Text Structural Principles by I. Engel Course Pack at Copy Center Web site https://www.umich.edu/~arch324 University of Michigan, TCAUP Structures II Slide 3/27

4. Course Schedule Lectures Monday & Friday video recorded and posted Homework web format Tests three total closed book closed notes Project tower Weight, height and load University of Michigan, TCAUP Structures II Slide 4/27

5. Design with Wood Code in the USA: NDS It is ASD and LRFD University of Michigan, TCAUP Structures II Slide 5/27 Source: American Forest & Paper Association, NDS: national design specification for wood construction : Washington, D.C. 2005 edition

6. Allowable Flexure Stress F b ’ F b from tables determined by species and grade F b ’ = F b (usage factors) usage factors for flexure: C D Load Duration Factor C M Moisture Factor C L Beam Stability Factor C F Size Factor C fu Flat Use C r Repetitive Member Factor Actual Flexure Stress f b f b = Mc/ I = M/S S = I /c = bd 2 /6 F b ’ >= f b University of Michigan, TCAUP Structures II Slide 6/27 Source: NDS 2005

7. Allowable Shear Stress Fv’ F v from tables determined by species and grade F v ’ = F v (usage factors) usage factors for shear: C D Load Duration Factor C M Moisture Factor Actual Shear Stress fv f v = VQ / I b = 1.5 V/A Can use V at d from support as maximum F v ’ >= f v University of Michigan, TCAUP Structures II Slide 7/27 Source: NDS 2005

8. Analysis Procedure Given: loading, member size, material and span. Req’d: Safe or Unsafe 1.Find Max Shear & Moment Simple case – equations Complex case - diagrams 2.Determine actual stresses f b = M/S f v = 1.5 V/A 3.Determine allowable stresses F b ’ and F v ’ (from NDS) 4.Check that actual < allowable f b < F’ b f v < F’ v 5.Check deflection 6.Check bearing (F b = R/A b ) University of Michigan, TCAUP Structures II Slide 8/27 Source: Structural Principles

9. Analysis Procedure Given: loading, member size, material and span. Req’d: Safe or Unsafe 1.Find Max Shear & Moment Simple case – equations Complex case - diagrams University of Michigan, TCAUP Structures II Slide 9/27

10. Analysis Procedure 2.Determine actual stresses f b = M/S f v = 1.5 V/A 2.Determine allowable stresses F b ’ and F v ’ (from NDS) 3.Check that actual < allowable f b < F’ b f v < F’ v 4.Check deflection 5.Check bearing (F b = R/A b ) University of Michigan, TCAUP Structures II Slide 10/27

11. Analysis Procedure Given: member size, material and span. Req’d: Max. Safe Load (capacity) 1.Assume f = F Maximum actual = allowable stress 2.Solve stress equations for force M = F b S V = 0.66 F v A 3.Use maximum forces to find loads Back calculate a load from forces Assume moment controls Check shear 4.Check deflection 5.Check bearing University of Michigan, TCAUP Structures II Slide 11/27 Source: Structural Principles

12. Analysis Procedure Given: member size, material and span. Req’d: Max. Safe Load (capacity) 1.Assume f = F Maximum actual = allowable stress 2.Solve stress equations for force M = F b S V = 0.66 F v A 3.Use maximum forces to find loads Back calculate a load from forces University of Michigan, TCAUP Structures II Slide 12/27

13. Analysis Procedure (cont.) 4.Use maximum forces to find loads Back calculate a load from forces Use P from moment to find Vmax 5.Check deflection 6.Check bearing University of Michigan, TCAUP Structures II Slide 13/27

14. Design Procedure Given: load, wood, span Req’d: member size 1.Find Max Shear & Moment Simple case – equations Complex case - diagrams 2.Determine allowable stresses 3.Solve S=M/F b ’ 4.Choose a section from S table Revise DL and F b ’ 5.Check shear stress First for V max (easier) If that fails try V at d distance from support If the section still fails, choose a new section with A=1.5V/F v ’ 6.Check deflection 7.Check bearing University of Michigan, TCAUP Structures II Slide 14/27 Source: Structural Principles

15. Design Procedure Given: load, wood, span Req’d: member size 1.Find Max Shear & Moment Simple case – equations Complex case - diagrams University of Michigan, TCAUP Structures II Slide 15/27

16. Design Procedure 2.Determine allowable stresses (given) 3.Solve S=M/F b ’ 4.Choose a section from S table Revise DL and F b ’ 5.Check shear stress First for V max (easier) If that fails try V at d distance (remove load d from support) If the section still fails, choose a new section with A=1.5V/F v ’ 6.Check deflection 7.Check bearing University of Michigan, TCAUP Structures II Slide 16/27

17. GRADING Visual Grading Each member is assessed for visual defects. (splits, knots, density, etc.) Machine Evaluated Lumber (MEL) Each member is assessed for density using x-ray technology. Machine Stress Rated (MSR) Each member is stressed by running it through rollers which measure the deflection and stiffness. The E modulus in bending can be calculated from the deflection. University of Michigan, TCAUP Structures II Slide 17/27

18. SIZE CATAGORIES University of Michigan, TCAUP Structures II Slide 18/27 Image Sources: Donald E. Breyer. Design of wood structures

19. SIZE CATAGORIES University of Michigan, TCAUP Structures II Slide 19/27 Donald E. Breyer. Design of wood structures. New York : McGraw- Hill, c1999. 4 th edition Source: Donald E. Breyer. Design of wood structures. New York: McGraw-Hill, c1999. 4 th edition

20. SIZE NOMINCLATURE Full Sawn The size delivered is the full nominal size Not generally available Rough Sawn Rough sawn condition with no surface planing Because no surfaces are planed, sizes are approximately 1/8” larger than S4S Dressed The size after shrinkage from drying and surface planing Typically dressed on all 4 sides S4S University of Michigan, TCAUP Structures II Slide 20/27 Full Sawn 2 x 4 Rough Sawn ~ 1 3/4 x 3 3/4 Dressed S4S 1 1/5 x 3 1/5

21. GROWTH CHARACTERISTICS Annual Rings Latewood is denser and stronger than earlywood. Sapwood is the actively living part of the tree. It is younger and transports water more readily than heartwood. The strength of the two is about the same. Density can be gauged visually by noting the % of latewood to earlywood Knots Knots result from tree branches Knots weaken the member and effect the grading University of Michigan, TCAUP Structures II Slide 21/27

22. Checks, Shakes and Splits All three are defects which weaken the wood Checks and splits are seasoning defects Shakes result from stress in the growing tree University of Michigan, TCAUP Structures II Slide 22/27

23. Slope of Grain The slope of the grain is taken in relation to the long edge of the member It is measured as a ratio e.g. 1” in 8” Increase in slope lowers the strength of the member University of Michigan, TCAUP Structures II Slide 23/27

24. Moisture Content MC = %water to oven dry wood In a living tree, MC can be 200% “free water” is contained in cell cavity “bound water” is within the cell wall Fiber Saturation Point (FSP) is the MC at 0% free and 100% bound water FSP is about 30% Equilibrium Moisture Content (EMC) is reached in service Shrinkage Shrinkage begins once MC<FSP Shrinkage is not the same in each direction Uncontrolled shrinkage results in splits University of Michigan, TCAUP Structures II Slide 24/27 Living tree FSP EMC

25. Engineered Wood Products Glulam Glue laminated lumber Stress rated and graded Parallel grain Different finish grades Standard widths and lams Straight or curved Size limit by transportation Stock or custom dimensions University of Michigan, TCAUP Structures II Slide 25/27 Source: NDS 2005

26. Engineered Wood Products Prefabricated Wood I-Joists ASTM D 5055 Standard dimensions Specifications per manufacturer University of Michigan, TCAUP Structures II Slide 26/27

27. Engineered Wood Products Structural Composite Lumber Laminated Veneer Lumber (LVL) Veneer ≤ ¼” Parallel Strand Lumber (PSL) Strand thickness ≤ ¼” Specifications per manufacturer University of Michigan, TCAUP Structures II Slide 27/27

28. Engineered Wood Products Wood Structural Panels Plywood – cross laminated wood veneer panels pressed and glued. Oriented Strand Board (OSB) – cross laminated layers of wood strands or wafers, compressed and glued Composite Panel – wood veneer and reconstituted wood based material University of Michigan, TCAUP Structures II Slide 28/27